CHEMICAL ENGINEERING TRANSACTIONS

VOL. 52, 2016

A publication of

The Italian Association of Chemical Engineering Online at www.aidic.it/cet

Guest Editors: Petar Sabev Varbanov, Peng-Yen Liew, Jun-Yow Yong, Jiří Jaromír Klemeš, Hon Loong Lam Copyright © 2016, AIDIC Servizi S.r.l.,

ISBN 978-88-95608-42-6; ISSN 2283-9216

Dimensionless Analysis of Heat, Momentum and Mass

Transfer in a Pool Fire

Luis G. Zárate*a, Mario E. Corderoa, Bulent Kozanoglub, Alejandro Regaladoc

aUniversidad Popular Autónoma del Estado de Puebla, 21 Sur 1103, Barrio de Santiago, 72410, Puebla, Puebla, México bUniversidad de las Américas-Puebla, Ex hacienda Santa Catarina Martir, 72820, Puebla, México cUniversidad del Mar, Ciudad Universitaria S/N, Puerto Ángel, Oaxaca, 70902, México

luis.zarate@upaep.mx

Statistical analysis about major accidents indicate that pool fires are among the most frequently encountered

major accidents in the Chemical Industry, cause the highest material and economical losses. The CFD

simulation has become an important research tool in this type of fires. Also hydrocarbons are first materials to

be ignited the first, in this paper, the phenomenon denominated as hydrocarbon pool fire is studied. The

hydrodynamics behavior considering the turbulent flow in transient regime were coupled with mass and heat

transfer transport including a generation of mas and energy due to a combustion reaction, where the chemical

kinetics considering the heptane as a surrogate compound for gasoline. The results are validated comparing

them with previously published experimental data, and show the presence of gradients of concentration,

temperature as well as velocity. In this type of scenarios, there are numerous dimensionless numbers which

can be used to describe the phenomena. These dimensionless groups provide the advantage of being able to

compare behaviors at different scales, where space and time variations are generally present. As a result

these dimensionless groups can be used in scaling analysis procedures.

1. Introduction

According to several statistical studies, pool fires represent a significant portion of major industrial accidents

(Casal, 2008). The Figure 1 present the problem denominated as hydrocarbon pool fire, the vast complexity in

these types of phenomena resides in hundreds of elemental chemical reactions with intermediate processes

that involve in a great number of chemical species simultaneously (Basevich, 2013). This type of study also

requires inclusion of momentum, mass and energy balances, and kinetically-influenced chemical reaction,

each one with wide range fluctuations of length scales (time and space). The flow might contain eddies down

to 10 –100 µm size and micro-timescale (Argyropoulos and Markatos, 2008). Thus, the prediction of the

behavior of these accidents is still being subject to numerous studies, and nowadays, computer simulation has

become one of the most important tools in search of feasible solutions (Vasanth et al., 2014). Particularly the

CFD model is effective to analyze some complicated accident scenarios that SFM (solid flame model), is not

capable of estimate (Sun et al., 2014) and useful to develop analysis of complex phenomena, which are very

hard to address experimentally (Raynal, 2015).

Pool fires had been widely studied during last few decades using different approaches, experimentally

(Mudan, 1984) or by computational simulation (Mishra, 2010). Although many of the studies mentioned above

are focused on a single aspect of the whole problem, some others tried to couple them by studying several

aspects of the phenomenon simultaneously (Faghri and Sunden, 2008). In this kind of research, both

experimental and theoretical studies are important; a better understanding of pool fires can be achieved only

through combining both approaches. Nevertheless, a complete pool fire predictive model that is applicable for

different pool sizes in an effective way has not been developed yet (Argyropoulos, 2015). The evident

complexity and variability inherent to pool fires are the principal factors for this poor development. Likewise,

the lack of experimental data for large pool sizes makes the theoretical models harder to validate (Skarsbo,

DOI: 10.3303/CET1652025

Please cite this article as: Zárate l. G., Cordero M. E., Kozanoglu B., Regalado A., 2016, Dimensionless analysis of heat, momentum and mass transfer in a pool fire, Chemical Engineering Transactions, 52, 145-150 DOI:10.3303/CET1652025

145

2011). Argyropoulos (2015) analyzes the literature of turbulent flows and notes that still has major failures in

the models of turbulent flows, it are still common for many applications particularly those that involve strong

curvature, intermittency, strong buoyancy influences, low-Reynolds-number effects, rapid compression or

expansion, strong swirl, and kinetically-influenced chemical reaction. While Raynal (2015) present an overview

of the simulation approaches and says it is frequently that mass and heat transfer and also chemical reactions

are not taken into account. This should be the main objective for the next decade to come.

(a) Experimental fire (b) Representation of the phenomena

Figure 1: Hydrocarbon pool fire whit a circular geometry

In this work was implemented a CFD simulation that consider simultaneously a momentum, mass and energy

transport balances, and including the combustion reaction and heat generation by reaction. This is an

important characterise of this model because in CFD and simulation literature the heat generation is usually a

constant volumetric term without the considering of activation energies and other important kinetic constants.

The control volume (CV) approach for a pool fire is used to develop a valid model and obtain velocity,

concentration and temperature profiles, which are used for get dimensionless groups, such as Reynolds and ,

Froude. Variables and dimensionless numbers, help to describe the characteristic behaviour of the flames

(geometry, energy transport, kinetic, composition).

2. Methodology

The approach of this paper is to simulate the different phenomena in the combustion zone. Coupled

momentum, mass and heat transfer equations are used for the CFD model. The momentum transfer is

simulated using the turbulent flow interface k - ϵ, while the mass transfer model includes the combustion

reaction of representative mixtures which have been proposed as surrogate for both gasoline and diesel

(Battin-Leclerc, 2008), considering a complete conversion and applying the combustion stoichiometry

proposed by Maron (1955). Also, the reaction rates and kinetic parameters given by Naidja (2002) are

included in the simulation. The effect of temperature has been considered over several transport parameters

and thermo physical constants, using AspenTech V 7.3 as well as MATLAB 7.8.

A selection of the kinetic parameters and properties used in this work are shown in Table 1 and Table 2

(thermodynamic properties, transport coefficients, kinetic parameters).The reaction stoichiometry used for the

combustion is shown below.

2.1 Kinetic model The fuel selected for this study was Heptane as a gasoline surrogate fuel, which follow the following reaction

stoichiometry:

2 2 22 2 2O CO H OFuel O CO H O

(1)

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The stoichiometry coefficients for heptane combustion are 2O = -11,

2CO = 7 and 2H O = 8 respectively. The

kinetic rate used in this work, is a modified version of single step Westbrook’s kinetics (Westbrook, 1984) and

showed in Eq(2).

expa bn

overal ar AT E RT Fuel Oxider

(2)

Table 1: Kinetic parameters for Heptane combustion

Parameter

A 5.1 × 1011

Ea [kcal/mol] 30

a 0.25

b 1.5

Table 2: Thermophysical and transport properties

Property value Property value 488.15K

rxnH 449,661.52 J mol fuel,mixD

6 27.297 10 m s

fuel

hmCp

25.51 J mol K 2O ,mixD

5 22.202 10 m s

2

0

OC

38.58 mol m 2CO ,mixD

5 21.677 10 m s

0

fuelC

312.96 mol m 2H O,mixD

5 22.403 10 m s

2

0

OV

9 m s mixk 1.181 W m K

0

fuelV

0.316 m s mix

33.233 kg m

fuel

vapG 20.4104 kg m s mixCp

1,183.71 J kg K

0

fuelm 0.725 kg s 0

3 13.43 10 K

0

fuelQ

30.602 m s

2.2 Transport models The CFD model is constituted by continuity, momentum, RANS turbulence model, mass and energy transport

equations. The respective equations are coupled and solved, considering that the phenomena occur

simultaneously. The mass transport model is using diffusion – convection whit generation by reaction on

transient mode for the i - species, where Di,M is the diffusivity coefficient of i – specie on the reacting mixture

and is showed in Table 2. In the energy case, the generation is given by:

gen rxn FuelQ H r (3)

3. Results and discussion

The results from CFD simulation in transient regime are presented in the Figure 2 to Figure 7. The

temperature values found fluctuated between 600 and 1,500 K with some maximum local values reaching

1,500 and 1,700 K. Generally, it was observed that the maximum temperature values of the flame are located

at the bottom (between 10 and 50 % of the total flame height), these results are very similar to reported in

literature (Chatris, 2001) and the behaviour register by Muñoz (2004). Figure 2 show the evolution in three

different instants whit geometries very different.

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(a) t = 0.58 s, Tmax = 1,125K (b) t =1.6 s, Tmax = 1,488K (c) t = 2 s, Tmax = 1,756K

Figure 2: Behaviour of the geometry and temperature profile in transient regime

In Figure 3 are presented in function of time the maximum temperatures encountered in different positions in

the combustion zone, and average temperatures of the simulated field, so this average temperature is a

temperature lower than located in the flames region. Therefore, it can be said that flame temperatures are

between these limits in the indicated instants.

Figure 3: Maximum temperatures and average temperatures across the simulated field

In the Figures 4(a) and 4(b) the behavior of Reynolds and Froude numbers are shown, respectively. In these

figures, a sharp increase is observed with Reynolds and Froude numbers at an elevation between 2.5 and 3.0

m, over the curve of 1.6 s. This deflection point corresponds in Figure 2(b), exactly where the maximum

temperature is observed. This can also be seen in Figure 5, where the temperature distribution is presented in

dimensionless form along the central axis. Noticed that at that moment (t = 1.6 s) other local maximum occurs

in the region located near the base (0.5 m approx.). The Figure 6 displays the reaction rate of the fuel in

mol/m3s, t = 1.6 s after the combustion started. This confirms the existence of combustion in the central region

with approximate height of 3 m because the reaction rate becomes a value different from zero. The values

found for the Reynolds number clearly show that the regime is highly turbulent, while the number value of less

than unit for Froude number indicates the importance of buoyancy forces.

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(a) Froude number (-) in the time 0 – 1.6 s (b) Reynolds number (-) between 0 to 1.6 s.

Figure 4: Dimensionless number along x=7.5 m, 0 6y m.

Figure 7 shows the reaction rate and the Froude number on the central axis of the Pool, plotting only up to 1 m

in height, this was done so to show that at the height of 0.45 m, coincided maximum temperature value (t = 2,

2.5, 3, 3.5, 4, 4.5 and 5 seconds with maximum values of temperature in K 1,756, 1,660, 1,623, 1,651, 1,567,

1,534, 1,491, respectively) an inflection is observed, although it also notes that are not maximum values Fr,

Re or Reaction rate. As shown in Figures displayed, the maximum temperatures do not coincide with the

maximum values of the dimensionless numbers or the reaction rate, however if inflections occur, it suggests

that the conditions to find the maximum values is a very complex phenomenon It depends on many variables

and non-linear behavior.

Figure 5. Dimensionless temperature along the

central axis in a pool fire.

Figure 6. Reaction rate of combustion of a

hydrocarbon at time 1.6 s.

(a) Reaction rate of combustion of a hydrocarbon (b) Froude number in a pool fire.

Figure 7: Reaction rate and Froude number in the time 0 ≤ t ≤ 5 s in the combustion of hydrocarbon pool fire

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4. Conclusions

The transient behaviour of a pool fire is approach by CFD, coupling models of mass, momentum and energy.

Present behaviours very similar to show in specialized literature with experimental data. The region of the

flames show fluctuations between 600 to 1,500K, while maximum temperatures values are present in regions

close to the base and below half the height of the flames, values between 1,500 to 1,700 K.

The selected kinetics is essential to obtain approximations of the temperature distribution, so the assumption

of a global and representative reaction is a simplification which translates into cost deviations from the exact

values in a fire. However it provides simulated data across the region, which comes closest to the actual

behaviour of a fire.

The dimensionless numbers, by definition, are valid regardless of the scales and thus are applicable in large-

scale fires and not only in pool fires of experimental sizes. The values of the Reynolds number are less than 1

× 105 in the low area, and for the temperatures maxims are 1 × 105 ≤ Re ≤ 5 ×105, these values of turbulence

are cause that flames are strongly distorted. The Froude number show small values in the region near to

surface area (Fr ≤ 1) and increases with the flame height, where the forces of momentum are dominant.

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